Towards single Ce ion detection in a bulk crystal for the development of a single-ion qubit readout scheme

Abstract

The work presented in this thesis was concerned with investigating the relevant spectroscopic properties of Ce ions randomly doped in an Y2SiO5 crystal at low temperatures (around 4 K), in order to develop a technique and an experimental set-up to detect the fluorescence photons emitted by a single Ce ion. The aim of the work was to determine whether a single Ce ion (referred to as the readout ion) can be used as a local probe to sense the quantum state of a neighbouring single-ion qubit via a state-selective interaction between the readout and qubit ion. More precisely, if the qubit ion is in state |1> or |0> state, the single Ce ion will, or will not, emit fluorescence photons. This single ion readout concept is a key step towards single-rare-earth-ion quantum computing, which is believed to be a promising approach for a scalable quantum computer.



Rare-earth ion based quantum computing is an attractive scheme for several reasons. Firstly, the qubit coherence time can be on the timescale of a minute while the optical coherence time can be on the millisecond timescale, despite the fact that the ions are in a solid (crystal), which means that more than 10000 optical pulses could be implemented before the system decoheres. Secondly, any sub-ensemble of ions in a frequency interval equal to or larger than the homogeneous linewidth within the inhomogeneously broadened absorption line can be used as a frequency-selectively addressed qubit. The proof of principle of the qubit-qubit interaction has been previously demonstrated. Thirdly, no special material engineering is required, and the crystal is commercially available. Ways of initializing a sub-ensemble of Pr ions as a qubit in the random system, manipulating the quantum state of the ions in a controlled way, and characterizing the quantum state created are presented.



In order to achieve better scalability, the idea of letting a single rare-earth ion represent a qubit was investigated. The fidelity of the single-ion readout scheme was briefly studied. The influence of the energy transfer process between two neighbouring ions on quantum computing is discussed.



A readout ion should possess a number of specific spectroscopic properties. Therefore, the position and the linewidths of the zero-phonon line of Ce ions were measured using an external cavity diode laser (at 371 nm) as the excitation source. The difference in the permanent dipole moment of the ground and excited states of Ce ions was measured in a photon echo experiment on Pr ions in a Ce-Pr co-doped Y2SiO5 crystal.



The last and most important task was to realize single Ce ion detection. Fluorescence of Ce ions has been detected from a crystal, where there is on average 1 ion within 4.6 \micro m$^3$ interacting with the excitation laser at a time. Estimates were made of the number of ions contributing to an observed signal. A trial experiment to investigate whether the signal was emitted by a single Ce ion was carried out, but was unsuccessful. Potential reasons why the experiment failed are presented.

Abstract (Swedish)

Popular Abstract in English

At the beginning of 20th century, scientists started to realize that atoms exhibited the discrete behaviour, e.g. the energies of bond electrons were not continuously distributed, but had discrete values. Light is also transmitted as discrete packages (called photons). These phenomena can not be explained by classical physics, which has been accepted as the law of describing the nature for hundreds of years, and a new theory, called quantum mechanics, was born.



Quantum mechanics has already made great changes to our lives. Two important applications are lasers and and transistors. Lasers are now used in many fields, for example in industry (laser cutting and laser lithography), in daily life (laser printers and DVD players), and in medicine (eye surgery, laser cosmetology and laser diagnosis). Transistors are the elementary electronic devices used for the logic gates in a computer, which can have one of two binary output values: 0 or 1. The invention of the transistor allowed the first general-purpose electronic computer, the Electronic Numerical Integrator and Computer, which weighed 30 tons, to be replaced by a modern computer weighing only a few kilograms. Transistor-based computers also have other advantages: they are faster, more reliable, cheaper to produce and consume less energy. Computers have become more and more compact, due to the decreasing size of transistors. However, there is a limit on the reduction in size of transistors, and the next step is to use single atoms.



The performance of computers based on single atoms will be determined by quantum mechanics. A so-called quantum computer will make use of the quantum properties of atoms to carry out computations. The primary information carrier is the quantum bit (called a qubit), which is a coherent superposition of two classical bits (i.e. it can have values of 0 and 1 at the same time). This allows computation to be vastly speeded up. For example, a two-qubit state can be in all four states: 00, 01, 10 and 11 simultaneously (with different probabilities), so a computational process using these two qubits can be implemented simultaneously on all four states at once. Using the classical two-bit computer, the same task has to be carried out four times. This so-called quantum parallelism may allow certain types of problems, which are currently difficult or almost impossible to solve on a conventional computer, to be easily solved on a quantum computer. For instance, factorizing a 300-digit integer to two prime numbers would take a conventional computer with a THz clock speed 150 000 years, even using the best algorithm, but this could potentially be done in less than 1 second on a large quantum computer. The RSA encryption algorithm, which is used, for example, to ensure security of online shopping using credit cards, is based on the presumed difficulty of factoring large integers, and the advent of quantum computers would thus render this algorithm useless. However, quantum computers are still confined to the realms of the research laboratory. As is the case with any new invention, it is difficult to predict how or when quantum computers will make an impact on the world.



The work described in this thesis is focused on developing a single-ion qubit readout scheme, with which a quantum computer with a large number of qubits could potentially be constructed. The `hardware' investigated consists of rare-earth ions (praseodymium or europium) doped in a transparent crystal. The qubit is represented by two of the hyperfine levels in the ground state of the ions. The electron population of these two states can be manipulated by optical laser pulses, using the excited state as an intermediate state. An arbitrary superposition state of a single qubit has been demonstrated. However, in this scheme each qubit consists of millions of ions, and all the ions in one qubit can not interact strongly with all the ions in another qubit, which imposes restrictions on the maximum number of qubits that can be used. Therefore, the use of a single ion as a qubit has been proposed, and simulations have shown that it is possible to construct a long chain of qubits using this scheme. However, it is necessary to develop a means of reading out the quantum state of a single-ion qubit.



The method currently being investigated in our group is co-doping another kind of rare-earth ion (cerium) into the same crystal as the qubit ions, and using a single Ce ion as a sensor (this can be pictured as a light bulb) to tell us which state the qubit ion (Pr) occupies via a controllable interaction between these two ions. If the Pr ion is in state 1, the `light bulb' will be turned on, sending out light (fluorescence). If the Pr ion is in state 0, the bulb will be turned off so no light will be seen.

• author: Yan, Ying
• supervisor: Stefan Kröll
• opponent: Prof. Bausá, Luisa, Departamento de Física de Materiales, Universidad Autónoma de Madrid, Spain
• organization: Atomic Physics; Linne Center for Nanoscience and Quantum Engineering-lup-obsolete (research group); NanoLund: Centre for Nanoscience
• publishing date: 2013
• type: Thesis
• publication status: published
• subject: Atom and Molecular Physics and Optics
• keywords: Fysicumarkivet A:2013:Yan, Ultra-violet laser spectroscopy, Single ion detection, Rare-earth-ion-doped crystals, Quantum computing, Laser stabilisation
• in: Lund Reports on Atomic Physics
• volume: LRAP-479
• pages: 185 pages
• defense location: Lecture Hall F (Fys: K404 ), Department of Physics, Professorsgatan 1, Lund University Faculty of Engineering.
• defense date: 2013-10-25 10:15:00
• ISSN: 0281-2762
• ISBN: 978-91-7473-699-1
• ISBN: 978-91-7473-700-4
• language: English
• LU publication?: yes
• id: d1bef1e5-46c1-4512-b9d4-ba8ef169b327 (old id 4068031)
• date added to LUP: 2016-04-01 13:51:50
• date last changed: 2019-05-21 18:10:44